%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT307+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:47:09 AM UTC 2026
% Result : ContradictoryAxioms 102.90s 25.65s
% Output : Refutation 102.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 16 unt; 0 typ; 1 def)
% Number of atoms : 75 ( 56 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 155 ( 22 ~; 20 |; 7 &; 94 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 ^; 52 !; 2 ?; 55 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(sk47_decl,type,
sk47: $i > $i > $i ).
thf(sk47_def,definition,
( sk47
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(984,plain,
! [A: $i,B: $i] :
( ( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(985,plain,
( ! [A: $i,B: $i] :
( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[984]) ).
thf(986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( D != k1_xboole_0 ) )
& ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( C != k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[985]) ).
thf(989,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[986]) ).
thf(993,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[989]) ).
thf(994,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[993]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(1182,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1183,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[1182]) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[1183]) ).
thf(1185,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1184]) ).
thf(1186,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk47 ) )
= A ),
inference(cnf,[status(esa)],[1185]) ).
thf(20620,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk47 ) )
= A ),
inference(lifteq,[status(thm)],[1186]) ).
thf(20621,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk47 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[994,20620]) ).
thf(20622,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk47 ) )
= A ),
inference(pattern_uni,[status(thm)],[20621:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(278,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(2029,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(2030,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[2029]) ).
thf(2031,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[2030]) ).
thf(20894,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ k1_zfmisc_1 ) )
| ~ ( k1_xboole_0 @ ( k1_xboole_0 @ sk47 ) @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[20622,2031]) ).
thf(20895,plain,
~ ( k1_xboole_0 @ ( k1_xboole_0 @ sk47 ) @ v1_xboole_0 ),
inference(pattern_uni,[status(thm)],[20894:[bind(A,$thf( C @ k1_zfmisc_1 )),bind(B,$thf( C ))]]) ).
thf(20921,plain,
! [B: $i,A: $i] :
( ( A
!= ( k1_xboole_0 @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( k1_xboole_0 @ sk47 ) )
= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[20622,994]) ).
thf(20922,plain,
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk47 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[20921:[bind(A,$thf( k1_xboole_0 @ ( C @ k2_zfmisc_1 ) )),bind(B,$thf( C ))]]) ).
thf(22073,plain,
~ ( k1_xboole_0 @ v1_xboole_0 ),
inference(rewrite,[status(thm)],[20895,20922]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(929,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(930,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[929]) ).
thf(931,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_xboole_0 )
| ( B != k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[930]) ).
thf(933,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[931]) ).
thf(935,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[933]) ).
thf(936,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[935]) ).
thf(22159,plain,
~ $true,
inference(rewrite,[status(thm)],[22073,936]) ).
thf(22160,plain,
$false,
inference(simp,[status(thm)],[22159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT307+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.38 % Computer : n005.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 25 20:41:02 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.71/1.71 % [INFO] Parsing done (718ms).
% 3.71/1.73 % [INFO] Running in sequential loop mode.
% 4.41/2.13 % [INFO] eprover registered as external prover.
% 4.41/2.13 % [INFO] Scanning for conjecture ...
% 5.62/2.46 % [INFO] Found a conjecture (or negated_conjecture) and 2960 axioms. Running axiom selection ...
% 8.09/3.10 % [INFO] Axiom selection finished. Selected 652 axioms (removed 2308 axioms).
% 10.00/3.70 % [INFO] Problem is first-order (TPTP FOF).
% 10.00/3.75 % [INFO] Type checking passed.
% 10.00/3.76 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 102.90/25.64 % [INFO] Killing All external provers ...
% 102.90/25.65 % Time passed: 25113ms (effective reasoning time: 23911ms)
% 102.90/25.65 % Axioms used in derivation (4): t113_zfmisc_1, t115_zfmisc_1, fc1_subset_1, d5_xboole_0
% 102.90/25.65 % No. of inferences in proof: 34
% 102.90/25.65 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 25113 ms resp. 23911 ms w/o parsing
% 102.90/25.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 102.90/25.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------